Contents
level: medium
The following important HDP chains were detected:
* DIS # B5: 4,5 => CTR => B5: 6,8,9 * DIS # F2: 1,9 => CTR => F2: 2,6 * DIS # F2: 1,9 => CTR => F2: 2,6 * DIS # F2: 1,9 => CTR => F2: 2,6 * DIS # I2: 8 => CTR => I2: 1,9 * DIS # D6: 2,8 => CTR => D6: 9 * DIS # A4: 2,8 => CTR => A4: 4,5,6,7 * DIS # B4: 2,8 => CTR => B4: 4,5,6 * PRF # D8: 2,8 => SOL * DIS # I8: 1,6 => CTR => I8: 2,4 * PRF # D8: 2,8 => SOL * CNT 11 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
The following important HDP chains were detected:
* DIS # B5: 4,5 => CTR => B5: 6,8,9 * DIS B5: 6,8,9 # F2: 1,9 => CTR => F2: 2,6 * DIS B5: 6,8,9 + F2: 2,6 # I2: 8 => CTR => I2: 1,9 * DIS B5: 6,8,9 + F2: 2,6 + I2: 1,9 # D6: 2,8 => CTR => D6: 9 * PRF B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 # D8: 2,8 => SOL * STA B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 + D8: 2,8 * CNT 5 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
..854.7.........3.1.9..84....1....9.....7.2......64.1...7....839.5..7.....43..9.. | initial |
3.854.7.....7...3.179.384....1....9.....7.2......64.1...74...83935..7.....43..97. | autosolve |
328541769456792831179638452741283596693175248582964317267459183935817624814326975 | solved |
level: medium
-------------------------------------------------- * PAIRS (14) B1: 2,6 A2: 4,5 B2: 4,5 C2: 2,6 F1: 1,9 D3: 2,6 H1: 2,6 I1: 1,9 G2: 1,8 C5: 3,6 C6: 2,3 D4: 2,8 A7: 2,6 G8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,F5: 1.. / D5 = 1 => 15 pairs (_) / F5 = 1 => 0 pairs (X) B7,B9: 1.. / B7 = 1 => 15 pairs (_) / B9 = 1 => 17 pairs (_) F1,I1: 1.. / F1 = 1 => 15 pairs (_) / I1 = 1 => 13 pairs (_) D5,D8: 1.. / D5 = 1 => 15 pairs (_) / D8 = 1 => 0 pairs (X) B1,C2: 2.. / B1 = 2 => 16 pairs (_) / C2 = 2 => 0 pairs (X) B1,H1: 2.. / B1 = 2 => 16 pairs (_) / H1 = 2 => 0 pairs (X) C2,C6: 2.. / C2 = 2 => 0 pairs (X) / C6 = 2 => 16 pairs (_) C5,C6: 3.. / C5 = 3 => 16 pairs (_) / C6 = 3 => 0 pairs (X) F4,F5: 3.. / F4 = 3 => 16 pairs (_) / F5 = 3 => 0 pairs (X) G4,G6: 3.. / G4 = 3 => 0 pairs (X) / G6 = 3 => 16 pairs (_) F4,G4: 3.. / F4 = 3 => 16 pairs (_) / G4 = 3 => 0 pairs (X) C5,F5: 3.. / C5 = 3 => 16 pairs (_) / F5 = 3 => 0 pairs (X) C6,G6: 3.. / C6 = 3 => 0 pairs (X) / G6 = 3 => 16 pairs (_) A2,B2: 4.. / A2 = 4 => 12 pairs (_) / B2 = 4 => 14 pairs (_) H8,I8: 4.. / H8 = 4 => 16 pairs (_) / I8 = 4 => 16 pairs (_) H5,H8: 4.. / H5 = 4 => 16 pairs (_) / H8 = 4 => 16 pairs (_) A2,B2: 5.. / A2 = 5 => 14 pairs (_) / B2 = 5 => 12 pairs (_) H3,I3: 5.. / H3 = 5 => 16 pairs (_) / I3 = 5 => 18 pairs (_) G7,I9: 5.. / G7 = 5 => 15 pairs (_) / I9 = 5 => 30 pairs (_) H3,H5: 5.. / H3 = 5 => 16 pairs (_) / H5 = 5 => 18 pairs (_) B1,C2: 6.. / B1 = 6 => 0 pairs (X) / C2 = 6 => 16 pairs (_) F2,D3: 6.. / F2 = 6 => 0 pairs (X) / D3 = 6 => 16 pairs (_) B1,H1: 6.. / B1 = 6 => 0 pairs (X) / H1 = 6 => 16 pairs (_) C2,F2: 6.. / C2 = 6 => 16 pairs (_) / F2 = 6 => 0 pairs (X) C2,C5: 6.. / C2 = 6 => 16 pairs (_) / C5 = 6 => 0 pairs (X) D3,D8: 6.. / D3 = 6 => 16 pairs (_) / D8 = 6 => 0 pairs (X) A4,A6: 7.. / A4 = 7 => 14 pairs (_) / A6 = 7 => 15 pairs (_) I4,I6: 7.. / I4 = 7 => 15 pairs (_) / I6 = 7 => 14 pairs (_) A4,I4: 7.. / A4 = 7 => 14 pairs (_) / I4 = 7 => 15 pairs (_) A6,I6: 7.. / A6 = 7 => 15 pairs (_) / I6 = 7 => 14 pairs (_) G2,I2: 8.. / G2 = 8 => 15 pairs (_) / I2 = 8 => 0 pairs (X) A9,B9: 8.. / A9 = 8 => 14 pairs (_) / B9 = 8 => 16 pairs (_) D8,E8: 8.. / D8 = 8 => 0 pairs (*) / E8 = 8 => 0 pairs (X) E4,E8: 8.. / E4 = 8 => 0 pairs (*) / E8 = 8 => 0 pairs (X) I1,I2: 9.. / I1 = 9 => 15 pairs (_) / I2 = 9 => 13 pairs (_) B5,B6: 9.. / B5 = 9 => 15 pairs (_) / B6 = 9 => 0 pairs (X) D5,D6: 9.. / D5 = 9 => 0 pairs (X) / D6 = 9 => 15 pairs (_) E7,F7: 9.. / E7 = 9 => 15 pairs (_) / F7 = 9 => 15 pairs (_) F1,I1: 9.. / F1 = 9 => 13 pairs (_) / I1 = 9 => 15 pairs (_) B5,D5: 9.. / B5 = 9 => 15 pairs (_) / D5 = 9 => 0 pairs (X) B6,D6: 9.. / B6 = 9 => 0 pairs (X) / D6 = 9 => 15 pairs (_) E2,E7: 9.. / E2 = 9 => 15 pairs (_) / E7 = 9 => 15 pairs (_) * DURATION: 0:00:49.123688 START: 23:51:28.062084 END: 23:52:17.185772 2019-04-30 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B2,C2,C5,C6,D3,D4,F1,G2,G8,H1,I1) * 3.854.7.....7...3.179.384....1....9.....7.2......64.1...74...83935..7.....43..97. * PAIR B1: 2,6 COL B B4: 2,6,4,5,8 # reduction candidate for 2,6 B4: 2,6 # 20 pairs B7: 2,6,1 # reduction candidate for 2,6 B7: 2,6 # 17 pairs B9: 2,6,1,8 # reduction candidate for 2,6 B9: 2,6 # 16 pairs * PAIR A2: 4,5 COL A A4: 4,5,2,6,7,8 # reduction candidate for 4,5 A4: 4,5 # 18 pairs A5: 4,5,6,8 # reduction candidate for 4,5 A5: 4,5 # 15 pairs * PAIR B2: 4,5 COL B B4: 4,5,2,6,8 # reduction candidate for 4,5 B4: 4,5 # 15 pairs B5: 4,5,6,8,9 # reduction candidate for 4,5 B5: 4,5 => CTR * 3.85497.1...71.8391796384....1..359...39712..592864317..74951839351876...1432.97. B5: 6,8,9 # 14 pairs * PAIR C2: 2,6 ROW 2 F2: 2,6,1,9 # reduction candidate for 2,6 F2: 1,9 => CTR * 32854.76...672..3.1796384....12.3.9...317524...296431...749.583935817624..435.971 F2: 2,6 # 16 pairs * PAIR F1: 1,9 BLK 2 E2: 1,9,2 # reduction candidate for 1,9 E2: 1,9 # 16 pairs F2: 1,9,2,6 # reduction candidate for 1,9 F2: 1,9 => CTR * 32854.76...672..3.1796384....12.3.9...317524...296431...749.583935817624..435.971 F2: 2,6 # 16 pairs * PAIR F1: 1,9 COL F F7: 1,9,2,5,6 # reduction candidate for 1,9 F7: 1,9 # 18 pairs F7: 2,5,6 # 15 pairs * PAIR D3: 2,6 BLK 2 F2: 2,6,1,9 # reduction candidate for 2,6 F2: 1,9 => CTR * 32854.76...672..3.1796384....12.3.9...317524...296431...749.583935817624..435.971 F2: 2,6 # 16 pairs * PAIR D3: 2,6 ROW 3 H3: 2,6,5 # reduction candidate for 2,6 H3: 2,6 # 18 pairs I3: 2,6,5 # reduction candidate for 2,6 I3: 2,6 # 16 pairs * PAIR D3: 2,6 COL D D8: 2,6,1,8 # reduction candidate for 2,6 D8: 2,6 # 17 pairs D8: 1,8 # 17 pairs * PAIR H1: 2,6 BLK 3 H3: 2,6,5 # reduction candidate for 2,6 H3: 2,6 # 18 pairs I3: 2,6,5 # reduction candidate for 2,6 I3: 2,6 # 16 pairs * PAIR H1: 2,6 COL H H8: 2,6,4 # reduction candidate for 2,6 H8: 4 # 16 pairs H8: 2,6 # 16 pairs * PAIR I1: 1,9 BLK 3 I2: 1,9,8 # reduction candidate for 1,9 I2: 8 => CTR * 328541769..67..138179638452..128..9..93175246..296431...74..583935..7624..435.971 I2: 1,9 # 15 pairs * PAIR G2: 1,8 BLK 3 I2: 1,8,9 # reduction candidate for 1,8 I2: 1,8 # 15 pairs I2: 9 # 13 pairs * PAIR D4: 2,8 BLK 5 E4: 2,8,5 # reduction candidate for 2,8 E4: 2,8 # 17 pairs D6: 2,8,9 # reduction candidate for 2,8 D6: 2,8 => CTR * 3.85497.1...71.8391796384....1..359...39712..592864317..74951839351876...1432.97. D6: 9 # 15 pairs * PAIR D4: 2,8 ROW 4 A4: 2,8,4,5,6,7 # reduction candidate for 2,8 A4: 2,8 => CTR * 3.854.7..45.7..83.179.384...41..36975.317.2..7...6431...74..583935..71....43..97. A4: 4,5,6,7 # 14 pairs B4: 2,8,4,5,6 # reduction candidate for 2,8 B4: 2,8 => CTR * 3.854.7.....7...3.179.384....1.5369...3.712....2.6431...74..5839351.7.....43..97. B4: 4,5,6 # 14 pairs * PAIR D4: 2,8 COL D D8: 2,8,1,6 # reduction candidate for 2,8 D8: 2,8 => SOLVED * 328541769456792831179638452741283596693175248582964317267459183935817624814326975 D8: 1,6 # 18 pairs * PAIR A7: 2,6 BLK 7 B7: 2,6,1 # reduction candidate for 2,6 B7: 2,6 # 17 pairs A9: 2,6,8 # reduction candidate for 2,6 A9: 2,6 # 16 pairs B9: 2,6,1,8 # reduction candidate for 2,6 B9: 2,6 # 16 pairs * PAIR A7: 2,6 ROW 7 F7: 2,6,1,5,9 # reduction candidate for 2,6 F7: 2,6 # 17 pairs F7: 1,5,9 # 14 pairs * PAIR A7: 2,6 COL A A4: 2,6,4,5,7,8 # reduction candidate for 2,6 A4: 2,6 # 19 pairs A4: 4,5,7,8 # 14 pairs * PAIR G8: 1,6 BLK 9 G7: 1,6,5 # reduction candidate for 1,6 G7: 1,6 # 30 pairs I8: 1,6,2,4 # reduction candidate for 1,6 I8: 1,6 => CTR * 3.854.7....67...3.179638425..1....9...317526.....64.1...74..583935..7.4...43..972 I8: 2,4 # 15 pairs I9: 1,6,2,5 # reduction candidate for 1,6 I9: 1,6 # 19 pairs * PAIR G8: 1,6 ROW 8 D8: 1,6,2,8 # reduction candidate for 1,6 D8: 2,8 => SOLVED * 328541769456792831179638452741283596693175248582964317267459183935817624814326975 D8: 1,6 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060615-absurd-base-pr-000.dot * REASONING * DIS # B5: 4,5 => CTR => B5: 6,8,9 * DIS # F2: 1,9 => CTR => F2: 2,6 * DIS # F2: 1,9 => CTR => F2: 2,6 * DIS # F2: 1,9 => CTR => F2: 2,6 * DIS # I2: 8 => CTR => I2: 1,9 * DIS # D6: 2,8 => CTR => D6: 9 * DIS # A4: 2,8 => CTR => A4: 4,5,6,7 * DIS # B4: 2,8 => CTR => B4: 4,5,6 * PRF # D8: 2,8 => SOL * DIS # I8: 1,6 => CTR => I8: 2,4 * PRF # D8: 2,8 => SOL * CNT 11 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B2,C2,C5,C6,D3,D4,F1,G2,G8,H1,I1) * 3.854.7.....7...3.179.384....1....9.....7.2......64.1...74...83935..7.....43..97. * PAIR B1: 2,6 COL B B4: 2,6,4,5,8 # reduction candidate for 2,6 B4: 2,6 # 20 pairs B7: 2,6,1 # reduction candidate for 2,6 B7: 2,6 # 17 pairs B9: 2,6,1,8 # reduction candidate for 2,6 B9: 2,6 # 16 pairs * PAIR A2: 4,5 COL A A4: 4,5,2,6,7,8 # reduction candidate for 4,5 A4: 4,5 # 18 pairs A5: 4,5,6,8 # reduction candidate for 4,5 A5: 4,5 # 15 pairs * PAIR B2: 4,5 COL B B4: 4,5,2,6,8 # reduction candidate for 4,5 B4: 4,5 # 15 pairs B5: 4,5,6,8,9 # reduction candidate for 4,5 B5: 4,5 => CTR * 3.85497.1...71.8391796384....1..359...39712..592864317..74951839351876...1432.97. * RESTART * PAIR B2: 4,5 COL B B4: 4,5,2,6,8 # reduction candidate for 4,5 B4: 2,6,8 # 18 pairs B4: 4,5 # 15 pairs * PAIR RESTART * PAIR B2: 4,5 COL B B4: 4,5,2,6,8 # reduction candidate for 4,5 B4: 2,6,8 # 18 pairs B4: 4,5 # 15 pairs * PAIR C2: 2,6 ROW 2 F2: 2,6,1,9 # reduction candidate for 2,6 F2: 1,9 => CTR * 32854.76...672..3.1796384....12.3.9...317524...296431...749.583935817624..435.971 * PAIR RESTART * PAIR F1: 1,9 COL F F7: 1,9,2,5,6 # reduction candidate for 1,9 F7: 1,9 # 18 pairs F7: 2,5,6 # 15 pairs * PAIR D3: 2,6 ROW 3 H3: 2,6,5 # reduction candidate for 2,6 H3: 2,6 # 20 pairs I3: 2,6,5 # reduction candidate for 2,6 I3: 2,6 # 18 pairs * PAIR D3: 2,6 COL D D8: 2,6,1,8 # reduction candidate for 2,6 D8: 2,6 # 19 pairs D8: 1,8 # 18 pairs * PAIR H1: 2,6 BLK 3 H3: 2,6,5 # reduction candidate for 2,6 H3: 2,6 # 20 pairs I3: 2,6,5 # reduction candidate for 2,6 I3: 2,6 # 18 pairs * PAIR H1: 2,6 COL H H8: 2,6,4 # reduction candidate for 2,6 H8: 4 # 18 pairs H8: 2,6 # 18 pairs * PAIR I1: 1,9 BLK 3 I2: 1,9,8 # reduction candidate for 1,9 I2: 8 => CTR * 328541769..6792138179638452..1..389..93175246..296431...74.95839358.7624284356971 * PAIR D4: 2,8 BLK 5 E4: 2,8,5 # reduction candidate for 2,8 E4: 2,8 # 20 pairs D6: 2,8,9 # reduction candidate for 2,8 D6: 2,8 => CTR * 3.85497.1...71.8391796384....1..359.5.39712...92864317..74...839351876...143..97. * RESTART * PAIR D4: 2,8 BLK 5 E4: 2,8,5 # reduction candidate for 2,8 E4: 5 # 26 pairs E4: 2,8 # 20 pairs * PAIR D4: 2,8 COL D D8: 2,8,1,6 # reduction candidate for 2,8 D8: 2,8 => SOLVED * 328541769456792831179638452741283596693175248582964317267459183935817624814326975 * DURATION: 0:00:21.408859 START: 23:52:50.711177 END: 23:53:12.120036 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060615-absurd-base-pr-001.dot * REASONING * DIS # B5: 4,5 => CTR => B5: 6,8,9 * DIS B5: 6,8,9 # F2: 1,9 => CTR => F2: 2,6 * DIS B5: 6,8,9 + F2: 2,6 # I2: 8 => CTR => I2: 1,9 * DIS B5: 6,8,9 + F2: 2,6 + I2: 1,9 # D6: 2,8 => CTR => D6: 9 * PRF B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 # D8: 2,8 => SOL * STA B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 + D8: 2,8 * CNT 5 HDP CHAINS / 30 HYP OPENED
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060615, absurd
See section Pair Reduction for the HDP chains leading to this result.
Full list of HDP chains traversed:
* INC # B4: 2,6 => UNS * INC # B7: 2,6 => UNS * INC # B9: 2,6 => UNS * INC # A4: 4,5 => UNS * INC # A5: 4,5 => UNS * INC # B4: 4,5 => UNS * DIS # B5: 4,5 => CTR => B5: 6,8,9 * INC # B5: 6,8,9 => UNS * INC # F2: 2,6 => UNS * DIS # F2: 1,9 => CTR => F2: 2,6 * INC # E2: 1,9 => UNS * DIS # F2: 1,9 => CTR => F2: 2,6 * INC # F2: 2,6 => UNS * INC # F7: 1,9 => UNS * INC # F7: 2,5,6 => UNS * INC # F2: 2,6 => UNS * DIS # F2: 1,9 => CTR => F2: 2,6 * INC # H3: 2,6 => UNS * INC # I3: 2,6 => UNS * INC # D8: 2,6 => UNS * INC # D8: 1,8 => UNS * INC # H3: 2,6 => UNS * INC # I3: 2,6 => UNS * INC # H8: 2,6 => UNS * INC # H8: 4 => UNS * INC # I2: 1,9 => UNS * DIS # I2: 8 => CTR => I2: 1,9 * INC # I2: 1,8 => UNS * INC # I2: 9 => UNS * INC # E4: 2,8 => UNS * DIS # D6: 2,8 => CTR => D6: 9 * INC # D6: 9 => UNS * DIS # A4: 2,8 => CTR => A4: 4,5,6,7 * INC # A4: 4,5,6,7 => UNS * DIS # B4: 2,8 => CTR => B4: 4,5,6 * INC # B4: 4,5,6 => UNS * PRF # D8: 2,8 => SOL * INC # D8: 1,6 => UNS * INC # B7: 2,6 => UNS * INC # A9: 2,6 => UNS * INC # B9: 2,6 => UNS * INC # F7: 2,6 => UNS * INC # F7: 1,5,9 => UNS * INC # A4: 2,6 => UNS * INC # A4: 4,5,7,8 => UNS * INC # G7: 1,6 => UNS * DIS # I8: 1,6 => CTR => I8: 2,4 * INC # I8: 2,4 => UNS * INC # I9: 1,6 => UNS * INC # D8: 1,6 => UNS * PRF # D8: 2,8 => SOL * CNT 51 HDP CHAINS / 51 HYP OPENED
Full list of HDP chains traversed:
* INC # B4: 2,6 => UNS * INC # B7: 2,6 => UNS * INC # B9: 2,6 => UNS * INC # A4: 4,5 => UNS * INC # A5: 4,5 => UNS * INC # B4: 4,5 => UNS * DIS # B5: 4,5 => CTR => B5: 6,8,9 * INC B5: 6,8,9 # B4: 4,5 => UNS * INC B5: 6,8,9 # B4: 2,6,8 => UNS * INC B5: 6,8,9 # B4: 4,5 => UNS * INC B5: 6,8,9 # B4: 2,6,8 => UNS * INC B5: 6,8,9 # F2: 2,6 => UNS * DIS B5: 6,8,9 # F2: 1,9 => CTR => F2: 2,6 * INC B5: 6,8,9 + F2: 2,6 # F7: 1,9 => UNS * INC B5: 6,8,9 + F2: 2,6 # F7: 2,5,6 => UNS * INC B5: 6,8,9 + F2: 2,6 # H3: 2,6 => UNS * INC B5: 6,8,9 + F2: 2,6 # I3: 2,6 => UNS * INC B5: 6,8,9 + F2: 2,6 # D8: 2,6 => UNS * INC B5: 6,8,9 + F2: 2,6 # D8: 1,8 => UNS * INC B5: 6,8,9 + F2: 2,6 # H3: 2,6 => UNS * INC B5: 6,8,9 + F2: 2,6 # I3: 2,6 => UNS * INC B5: 6,8,9 + F2: 2,6 # H8: 2,6 => UNS * INC B5: 6,8,9 + F2: 2,6 # H8: 4 => UNS * INC B5: 6,8,9 + F2: 2,6 # I2: 1,9 => UNS * DIS B5: 6,8,9 + F2: 2,6 # I2: 8 => CTR => I2: 1,9 * INC B5: 6,8,9 + F2: 2,6 + I2: 1,9 # E4: 2,8 => UNS * DIS B5: 6,8,9 + F2: 2,6 + I2: 1,9 # D6: 2,8 => CTR => D6: 9 * INC B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 # E4: 2,8 => UNS * INC B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 # E4: 5 => UNS * PRF B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 # D8: 2,8 => SOL * STA B5: 6,8,9 + F2: 2,6 + I2: 1,9 + D6: 9 + D8: 2,8 * CNT 30 HDP CHAINS / 30 HYP OPENED